CHAOTIC SYSTEM BASED MODELLING OF TRI-ECHELON SUPPLY CHAIN AND ITS SYNCHRONIZATION

Abstract

This study presents a comprehensive mathematical model of a tri-echelon supply chain system, aimed at understanding and mitigating the bullwhip effect—a well-known phenomenon in supply chain management where small fluctuations in consumer demand lead to increasingly larger variances in orders placed upstream in the supply chain. The model incorporates exponential non-linearity to accurately capture the real-world behaviour of demand variability amplification. Unlike traditional linear models, the introduction of non-linear components allows for a more realistic representation of supply chain dynamics, especially under conditions of uncertainty and varying lead times. This non-linearity serves to simulate the compounding nature of demand signals as they propagate from the retailer to the wholesaler and finally to the manufacturer. To validate the effectiveness and robustness of the proposed model, a thorough numerical analysis has been carried out. This includes sensitivity analyses with respect to key system parameters, such as lead time, ordering policies, and inventory adjustment rates. The results demonstrate that the model not only replicates the bullwhip effect under conventional assumptions but also reveals insights into how specific factors contribute to or mitigate the effect. These findings provide a solid foundation for developing advanced control mechanisms aimed at synchronizing supply chain operations. In addition to the mathematical formulation and analysis, an adaptive control synchronization scheme has been designed to ensure coordinated behavior across the three echelons of the supply chain. This scheme leverages real-time system feedback to adjust control parameters dynamically, enabling the system to respond efficiently to external disturbances and internal fluctuations. The adaptive nature of the controller makes it suitable for practical deployment, where system parameters may not be precisely known or may change over time due to market conditions. To further substantiate the theoretical developments, extensive computer simulations have been conducted. These simulations illustrate the dynamic behavior of the supply chain model under various scenarios and confirm the correctness, stability, and robustness of the proposed control scheme. The outcomes highlight the potential of the model as a valuable tool for both academic research and industrial application in optimizing supply chain performance and mitigating the adverse effects of demand variability.